// Problem 055: Lychrel numbers

// If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
// Not all numbers produce palindromes so quickly. For example,

// 349 + 943 = 1292,
// 1292 + 2921 = 4213
// 4213 + 3124 = 7337

// That is, 349 took three iterations to arrive at a palindrome.
// Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
// Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
// How many Lychrel numbers are there below ten-thousand?

package main

import (
	"fmt"
	"math/big"
	"projecteuler/euler"
)

func isLychrel(number int) bool {
	current := big.NewInt(int64(number))
	reverse := big.NewInt(0)

	for i := 0; i < 50; i++ {
		reverse.SetString(euler.ReverseString(current.String()), 10)
		current.Add(current, reverse)
		if euler.IsPalindromeString(current.String()) {
			return false
		}

	}

	return true
}

func p055() {
	ans := 0
	for i := 0; i < 10000; i++ {
		if isLychrel(i) {
			ans++
		}
	}
	fmt.Println("Problem 055:", ans)
}
